A major consideration in any propellant development program is the characterization of the burning rate. Typically, burning propellant strands and subscale motor firings have been the means by which this information has been obtained. Of the two methods, experience has shown that subscale motors provide the better approximation of actual full scale motor conditions. To characterize the burning rate of the propellant as a function of pressure, a minimum of two subscale motor firings are required. But more typically, to insure statistical accuracy, from 3 to 9 or more firings are performed.
The typical subscale motor is designed to produce a neutral pressure-time history, and thus operate at a relatively constant pressure and burning rate. The average burning rate over the duration of a motor firing is typically determined by dividing the web distance burned by the burn time. The determination of burn time varies throughout the industry, but is typically based on the intersection of an aft tangent bisector with the pressure-time trace of a motor. This method of determining burning rate takes little advantage of internal ballistic information available from a subscale motor firing. Therefore, each subscale motor firing produces only a single pressure-burning rate point based on a determination of average conditions during a motor firing. The burning rate behavior of the propellant is thus characterized by firing a series of subscale motors over a range of operation pressures to provide several pressure-time burning rate points.
There are two obvious shortcomings involved in using the conventional subscale motor to determine burning rate. These are:
1. Several motor firings are required to characterize a propellant. PA0 2. Burning rate determinations do not fully utilize the available internal ballastic information.
Ballistic test motors that are used throughout industry may be, generally, classified as those that have neutral pressure-time traces, as noted hereinabove, and those that do not. For the neutral burning motors, a survey on burning rate determination methodology has been performed industry-wide and is discussed in detail by W. T. Brooks in "Proposed Standardized Method for Correlating Subscale Motor Burn Rates," CPIA Publication No. 300, Chemical Propulsion Information Agency, Laurel, MD, May 1979.
While neutral burning test motors are the most commonly used test motors in industry, some motors that have non-neutral traces are employed. Of these motors, a stepped grain motor has been employed that produces a pressure-time trace as a series of steps. Initially, the motor operates at a first relatively constant pressure for a period of time and then abruptly changes to lower pressures, sequentially, as the burning surface area periodically changes. Since the stepped grain motor operates essentially as a series of neutral burning motors incorporated into a single propellant grain, the methods used for analyzing neutral traces can be applied for characterizing the burning rate.
An externally burning propellant slab may also be used as the grain of the non-neutral test motor. The slab produces a regressive pressure-time trace. In the slab burner process the pressure-time trace of the motor is used to determine instantaneous burning rate data. The geometry of the slab is initially known and an internal ballastic model of the motor is used to track the geometric regression of the slab. The ballistic model is used at each point in time to determine the geometry required to satisfy the continuity equation for the given instantaneous operating pressure. The burning rate at a given time step is determined by considering the amount of web distance burned over the past time step that is required to produce the appropriate geometry to satisfy continuity. Thus, the motor produces a series of instantaneous burning rate points that correspond to the pressure-time trace. These data points are then curve fitted to obtain a burning rate law.
After considering the existing methodology for obtaining burning rate data from ballistic test motors, it is evident that a need exists for an improved method. The neutral-burning test motors are attractive because they are simple to manufacture, and the data reduction process that is required is straightforward. However, these motors have two major shortcomings. The first is based on the neutrality of the motor--the motor operates at a relatively constant pressure, and thus can produce only a single, average, burning rate-pressure data point. Therefore, several motor firings are required to characterize a propellant.
The second shortcoming occurs in the way by which the average burning rate is determined. Several methods of determining burning rate may be used. A problem arises because the value of burning rate determined from a given trace will vary with the reduction method employed. In fact, if the aft-tangent method is employed (which is the most common method used) the value of burning rate can vary with the person reducing the data. Hence, a problem exists because these burning rates are based on definitions that are somewhat arbitrary; therefore, the data is subject to the definition chosen. A detailed consideration of the variability introduced by the reduction method chosen is presented by W. T. Brooks in "Workshop Report; "Burn Rate Determination Methodology," CPIA Publication No. 347, Chemical Propulsion Information Agency, Laurel, MD, October 1981, pp. 261-277.
Regardless of the method employed to obtain the propellant burning rate, a neutral trace motor still produces only a single data point. This problem can be overcome by employing a non-neutral trace motor. However, the stepped grain motor analysis process is essentially the same as that for a neutral motor. Therefore, the use of this motor incorporates the shortcomings experienced in using a neutral motor. In addition, the number of data points produced by the step is limited to the number of steps incorporated in the stepped design.
The slab burner approach eliminates several of the problems encountered in the stepped grain motor. The motor has a regressive pressure-time trace and thus operates over a range of pressures. Thus a burning rate-pressure data point can be produced at each time step on the pressure-time trace. In addition, the burning rate data is produced by an internal ballistic model and thus is not subject to any arbitrary definitions. The slab burner does have the problem that the burning-rate data is extremely sensitive to the pressure data, as the burning rate is computed directly from the pressure-time data. Any noise, or fluctuations in the data will be directly reflected in the burning rate data. In addition, these errors will be introduced into the geometry model and thus further compound the error.